The Royal Navy is to have seven of the new Astute-class boats – two are undergoing sea trials and a third is near completion.

Just under half of the money announced on Monday will be spent on building the fourth of the submarines; the rest will to used to buy the equipment and materials needed for the remaining three boats.

The decision will secure 3,000 jobs at the dockyards in Barrow-in-Furness where the Astutes are being built by BAE Systems.

The programme, which has been beset by difficulties since it was commissioned in 1997, is expected to cost up to £10bn for a fleet that is already years late.

Last month, the Guardian revealed that during sea trials, the first of the class, HMS Astute, had suffered problems that raised questions about the performance and reliability of the boat.

HMS Astute cannot reach the top speed the MoD boasted it could, sprang a leak that required it to perform an emergency surfacing, and was fitted with electrical circuit boards that failed the navy's safety standards.

A lead-lined water jacket, which surrounds the submarine's nuclear reactor, was also constructed with metal of the wrong quality. And the living quarters for the 98-strong crew are also more cramped than those on submarines made more than 50 years ago.

The Astute ran aground two years ago, a calamity that led to the removal of its commander.

However, the navy is adamant the vessel can overcome the difficulties, and that the three years of rigorous sea trials – which have not yet been completed – will give engineers time to iron out the problems. It says such issues are to be expected in a "first in class", especially as the boats are the navy's most technically advanced.

Some critics have said the Astute programme would have been scrapped years ago but for the need to maintain a submarine-building capability at Barrow – where replacements for the Trident-carrying Vanguard boats are likely to be constructed.

Rear Admiral Simon Lister, the MoD's director of submarines, said the Astute would become "the jewel in the crown" of the Royal Navy's submarine fleet. "These submarines represent a huge leap forward in technology and will operate all over the world with the Royal Navy. These boats provide the optimum capability a submarine can offer in land strike, strategic intelligence gathering, anti-submarine and surface ship warfare, and protection of the strategic deterrent," he added.

The defence secretary, Philip Hammond, said: "This funding demonstrates our commitment not only to a key Royal Navy capability, but also to the submarine industry in Barrow, which will play a vital role in Britain's defence for decades to come."